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Perturbed Markov chains

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  14 July 2016

Eilon Solan  and
Nicolas Vieille
Eilon Solan*
Affiliation:
Northwestern University and Tel Aviv University
Nicolas Vieille*
Affiliation:
HEC, Jouy-en-Josas
*
∗ Postal address: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
∗∗ Postal address: Département Finance et Economie, HEC, 1, rue de la Libération, 78 351 Jouy-en-Josas, France. Email address: [email protected]
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Abstract

We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.

Keywords

Markov chainsstationary distributionexit distributionconductancesensitivity analysisperturbation theorystability of a Markov chain

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60F10: Large deviations
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 107 - 122
Copyright
Copyright © Applied Probability Trust 2003 

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